ConjugateInversion

Conjugate Inversion

Consider two inversions with respect to two circles z(Z) and x(X): Inv_Z, Inv_X. Then the conjugate transformation f = (Inv_Z)*(Inv_X)*(Inv_Z) is equal to the inversion Inv_W, with respect to circle w(W), which is the inverse of circle x(X) with respect to z(Z). Thus z(Z) is the [Inversion interchanging] circles x(X) and w(W), and we have
(Inv_Z)*(Inv_X)*(Inv_Z) = (Inv_W) <== > (Inv_Z)*(Inv_W) = (Inv_X)*(Inv_Z).

This fact on inversions is used in the file MidCircleInverted.html to prove that inversions preserve the [Inversion interchanging property] of a circle.

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